I've never owned or driven a 4x4 so I don't know much about either but if I was going to buy one, it'd be a push-button. I like electronics and I wouldn't do any super-serious off-roading with it anyway.

HA! My vote tied it up.
I had the lever in my 89, 94, my 96 had the pushbuttons, my 11 has the rotary knob.
Whether you have the floor or push button the front hubs are still electronic. So that part does not matter. My 96 I had for 17 years and 300K+ miles with a lot of that off road. Never had a problem with shifting in or out of 4 wheel drive or 4 Lo. What I did not like with the lever is that you must be moving at 1-3mph in neutral to get in or out of 4 Lo. The electronic will go in or out of 4 Lo even sitting still. Yes there is a big clunk that sounds like something is gonna break when it does, but at least it does do it. With the lever, if I was already stuck it would not go into 4 Lo at all.

On partially snow covered roads the auto 4x4 is great. it does not reduce MPG much to have it on, where 4x4 cuts gas mileage in half.

People talk about push button like they fail all the time. I've driven multiple 2008+ 4wd trucks and suvs and never had the slightest hint of failure.

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Exactly! Owned (or leased) countless 4x4s (Trucks, SUVs) that had push button...and never had a problem with a button failing. I love the Auto 4x4 option as well. Let the computer determine if there is any slippage and engage 4x4 as needed. My first vehicle in high school was an 84 Jimmy... and I remember having to either stop or go really slow to engage 4-LO or disengage it or something? Same on a 89 Toyota P/U I had with the floor lever (and I had to get out and lock hubs). OR I can sit in the truck and push a button and let the truck do it and determine when I need 4x4. Yeah, give me the push button.